Friday, October 18, 2013

Does God Know Pi?

TL;DR: Yes He does, and it is always best to read in context.

Does the God of the Bible know the value of Pi? 1 Kings portrays the building of the temple under Solomon. Among the sacred accoutrements is a large brass (or bronze) bowl for ceremonial washing. An apparent discrepancy was brought to my attention on an atheist’s blog a few years ago. The passage in question is 1 Kings 7:23And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.” This verse gives three measurements for the molten sea; a diameter (d) of 10 cubits, a depth of 5 cubits, and a circumference (C) of 30 cubits. Now, any junior high math student knows that the circumference of a circle is Pi times the diameter. Pi is a mathematical constant normally rounded to 3.14159 (if you want a more exact estimate, check this link). Clearly if the diameter is 10 cubits, the circumference should be about 31.4 cubits. Could the Bible, if truly inspired by an omniscient God, portray a 1.4-cubit discrepancy on such an elementary concept? Let’s face it, it’s less than 5% right? But some apologists have tried to grapple with the discrepancy with a variety of explanations, the most creative of which is gematria with the spelling of the Hebrew words. But, as we will see, these kinds of shenanigans are wholly unnecessary.

Before moving to resolve the issue, a little bit on ancient measurements: A Biblical cubit is an anthropic unit equivalent to about 18 inches, derived from the measurement from a man's elbow to the tip of his middle finger. Another such unit is the hand breadth still in use in equestrian circles today, equal to 4 inches. A hand breadth is mentioned just a few verses later in 1 Kings 7:26, “And it was an hand breadth thick, and the brim thereof was wrought like the brim of a cup, with flowers of lilies: it contained two thousand baths.” This verse introduces additional information about the laver, it’s thickness (t).

Could it be that the discrepancy between the diameter and the circumference are made up in the thickness? For this to be the case, the circumference given would be the interior circumference and the correlating diameter should be 10 cubits minus 2-hands worth of thickness. If this is correct, Pi should be found by dividing the circumference by the interior diameter.

C / (d – [2 x t]) = π                                            eq. 1

To make it easy the dimensions are boiled down  to something familiar:

d = 10 cubits = 180 inches
C = 30 cubits = 540 inches
t = 1 hand breadth = 4 inches

and applying equation 1:

 540 / (180 – ([2 x 4]) = 3.139535                  eq. 2

The result is not exactly Pi, but within 0.07%, well within the constraints of significant digits and, dare I say, nothing to squabble over when talking units based on human proportions. That 1 Kings 7:23 is speaking of the external diameter and the internal circumference becomes pretty clear. So, not only does the God of the Bible know the value of Pi but this example can be used as a reminder to look at these things in context before turning to esoteric speculation and desperate rationalization.

 Items for further investigation:
·     The volume for the laver is given later in the chapter, the traditional unit conversions do not match.

Thursday, October 17, 2013

How Many People Crossed the Red Sea?

TL;DR: An estimated 1.66 million people crossed the Red Sea.

The goal of this post is to determine if the Bible gives the quantity of people who crossed the Red Sea. Exodus 12:37 gives a number of 600,000 men leaving Egypt on foot. The task is to determine a multiplier which will give an estimate to include women and children.

Besides the 600,000 listed in Exodus 12:37, no other population details are provided for this event. However, there are other passages where details are given as the focus of the book. Numbers 2 lists the number of fighting men except for the tribe of Levi. With this exception, there are 603,550 fighting men listed. This number of fighting men seems to correlate by order of magnitude and role to the 600,000 from Exodus 12:37, additionally Exodus 13:18 says that Israel went up in martial array (NASB) from the land of Egypt. The following table is a breakdown of the fighting men from each tribe and the total.

Table 1. Numbers 2 census of fighting men.

Numbers 2:3, 4
Numbers 2:5, 6
Numbers 2:7, 8
Numbers 2:10, 11
Numbers 2:12, 13
Numbers 2:14, 15
Numbers 2:18, 19
Numbers 2:20, 21
Numbers 2:22, 23
Numbers 2:25, 26
Numbers 2:27, 28
Numbers 2:30, 31
Numbers 2:32

Numbers 3 compares the number of first-born men in all of Israel (vs. 43) to the number of Levite men one month and older (vs. 39). Of the tribes, Levi is the only one where the total number of men is stated without qualifiers, e.g. "fighting men" or "first born." Levite men numbering 22,000 will serve as a baseline by comparing Levite subsets to the whole. One such subset is given in Numbers 4:48 where the number of Levite men between the ages of 30 and 50 years of age is given as 8,580. The ratio of total Levite men one month and up to those ages 30 to 50 will be used to extrapolate total males of Israel and later total population. Ages 30 to 50 is a 20 year span. By dividing the number of Levites between ages 30 and 50 by the number of years, an average number of Levite men per 1-year age group ages 30 to 50 can be found.

50 - 30 = 20 years
eq. 1

8,580 / 20 = 429 per 1-year age group
eq. 2

Next, a number of men per 1-year age group must be found for those outside of the ages 30 to 50. To accomplish this, we must know the life expectancy of the average Levite. Psalm 90:10, which is accredited to Moses (a Levite), says, "The days of our years are three score years and ten; and if by reason of strength, they may be four score years yet is their strength labour and sorrow; for it is soon cut off, and we fly away." (KJV). That is, 70 years or 80 if by strength. For the purposes of estimating, 75 will be used as an average. Since we know that the Levite men between the ages of 30 and 50 number 8,580, the remaining 13,420 (that is 22,000 - 8,580) are spread between the ages of 0 and 30 and 50 and 75.

13,420 / (30 + [75 - 50]) = 244 per 1-year age group
eq. 3

Now these proportions of the tribe of Levi will be applied to the rest of Israel's population. The life expectancy of a Levite was determined above, however Deuteronomy 2:14 and 16 gives a clue as to the life expectancy of the fighting men in that it took 38 years for all of the fighting men to perish from Israel, just "as the Lord had sworn to them." Numbers 14:29 gives the details of the Lord's oath, "your carcases shall fall in this wilderness; and all that were numbered of you, according to your whole number, from twenty years old and upward, which have murmured against me." (KJV). From this verse, it is clear that those who fell were those who were numbered (Numbers 2) and that those who were numbered were twenty years old and up. The minimum age of fighting men is confirmed in Numbers 26 where it describes a re-count of those men able to go to war (vs. 2) and specifies 20 years and over. Adding 20 to 38 gives a life expectancy of 58 years old.

Having established the age range of the fighting men as 20 to 58 years, the correlating number of Levites from age 20 to 58 must be determined. Multiplying the number of men per 1-year age group times the number of years ages 20 to 30 and 50 to 58 (18 years) and adding them to the known 8,580 figure found in Numbers 4:48 gives the number of Levites 20 to 58 years.

18 x 244 + 8580 = 12,972 Levite men between 20 and 58
eq. 4

To complete the ratio, the total number of Levite men from 1 month to 58 must be determined.

(30 + [58 – 50]) x 244 + 8580 =  17,852 Levite men 1 month to 58 years
eq. 5

The ratio of Levite men age 1 month to 58 to Levite men age 20 to 58 to then is:

17,852 / 12,972 = 1.3762 ratio
eq. 6

Using this ratio, multiplying the number of fighting men 603,550 (Numbers 2:32) by 1.3762 gives 830,602 total men of the other tribes 1 month and up. Because Numbers 2 does not count the Levite men, 22,000 must be added to 830,602 to obtain a total of 852,602 men age 1 month and up. Assuming an equal count for each gender, this number is doubled to 1,705,204 for the total Numbers 2-4 population. The Red Sea crossing and Numbers 2-4 occurred about two years apart so the numbers will be different. Making assumptions about demographic stability, again calculate a ratio of fighting men to Israel as a whole. Because the Levites were not set apart until Numbers 3, we will assume the Levites are included in the number of men leaving Egypt on foot in Exodus 12:37. To accommodate this, add the Numbers 2 number of fighting men to the estimated number of Levites of the same age.

603,550 + 12,972 = 616,522 number of men age 20 to 58

eq. 7
1,705,204 / 616,522 = 2.7658 ratio of total population to men age 20 to 58

eq. 8
In conclusion, multiplying 2.7658 times the 600,000 described in Exodus 12:37 gives an estimated population crossing the Red Sea as 1.66 million people.

 Items for further investigation:

·        The estimates for Israel's population have a bulge between the ages of 20 and 58 resulting from the Levite tallies (Numbers 3:39 and Numbers 4:48). This is counter-intuitive.
·        There is a large variation between Moses' observation in Psalm 90:10 and the life expectancy of fighting men derived from Deuteronomy 2:14, 16 and Numbers 14:29 and even Moses' own lifespan provided in Deuteronomy 34:7.
·        The number of Israel's first born in Numbers 3:43 (not covered here) appears to be extremely low.
·        The implications on the miracle of dividing the Red Sea.
·        How these ratios can be applied to other passages like the feeding of the 5000 in Matthew 14:21, Mark 6:44, Luke 9:14, John 6:10.

Suggestions? Have I made a mistake? Have I missed a crucial passage? Comment below.

Monday, October 14, 2013

The Children of Adam, Introduction

Introducing a Biblical genealogy project using the mind mapper software FreeMind to chart out the genealogies given in the Bible. I've started with with Genesis and will be working through into the Gospels of the New Testament. My goal is to provide a fully referenced genealogy as a tool for understanding the backgrounds of the people and nations portrayed in the Bible. The work in progress can be accessed at the following link:

There are a few notes that will help in understanding the diagram.
  • Yellow highlights indicate those patriarchs for which ages are provided and can be used later to develop a Biblical age of the earth.
  • Light-green boxes indicate nations/clans/tribes.
  • Pink highlights indicate women.
  • Red arrows indicate marriages.
  • There is a tread of kings or chiefs of Edom, gold arrows indicate where individuals fit into the line of rulers.
  • Light-gray arrows indicate interactions.
  • Clicking on a name will collapse or expand the diagram.
  • Click and drag mouse controls as well as wheel scroll are enabled to zoom and pan.
  • The box at the center of the button cluster at the top left allows for a search.
  • The button cluster at the top center has the following functions in order from left to right:
    • Back
    • Forward
    • Increase
    • Shrink
    • Fit
    • Reset
    • Shadow On (not recommended)
    • Hot Key Assignments
    • Background Colors


This post is to set up the category labels.